How can I cut an edge from a plane?
It could be a CtrlShiftB, 1-segment Vertex Bevel:

You can adjust to precision in the operator's F9 Adjust Last Operation panel.
Thanks to @John Eason for the reminder.. While modelling, always have your object's Scale CtrlA applied to (1,1,1) for predictable results from operations and modifiers.
Edit: The shipped add-on 'TinyCAD' can find the projected intersections between lines, and insert vertices at the closest approach. If you have a lot of that to do, you could set up shortcuts for that.
Without add-ons, this could be a way? There's probably a better one..

With Snap set.. 'To: Vertex' and 'With: Active'

K cut an arbitrary edge, to insert vertices
ShiftD duplicate the vertices of the template edge.
GX with and GY, switching active vertices, snap to the target corner, one dimension at a time
Snap the pre-cut vertices to the duplicate, and M &gt; 'By Distance' merge everything down.